4 Subsetting

4.1 Introduction

R’s subsetting operators are fast and powerful. Mastering them allows you to succinctly perform complex operations in a way that few other languages can match. Subsetting in R is easy to learn but hard to master because you need to internalise a number of interrelated concepts:

Subsetting is a natural complement to str(). While str() shows you all the pieces of any object (its structure), subsetting allows you to pull out the pieces that you’re interested in. For large, complex objects, I highly recommend using the interactive RStudio Viewer, which you can activate with View(my_object).

Quiz

Take this short quiz to determine if you need to read this chapter. If the answers quickly come to mind, you can comfortably skip this chapter. Check your answers in Section 4.6.

What is the result of subsetting a vector with positive integers,
negative integers, a logical vector, or a character vector?

What’s the difference between [, [[, and $ when applied to a list?

When should you use drop = FALSE?

If x is a matrix, what does x[] <- 0 do? How is it different from
x <- 0?

How can you use a named vector to relabel categorical variables?

Outline

Section 4.2 starts by teaching you about [.
You’ll learn the six ways to subset atomic vectors. You’ll then
learn how those six ways act when used to subset lists, matrices,
and data frames.

Section 4.3 expands your knowledge of subsetting
operators to include [[ and $ and focuses on the important
principles of simplifying vs. preserving.

In Section 4.4 you’ll learn the art of
subassignment, which combines subsetting and assignment to modify
parts of an object.

Section 4.5 leads you through eight important, but
not obvious, applications of subsetting to solve problems that you
often encounter in data analysis.

4.2 Selecting multiple elements

Use [ to select any number of elements from a vector. To illustrate, I’ll apply [ to 1D atomic vectors, and then show how this generalises to more complex objects and more dimensions.

4.2.1 Atomic vectors

Let’s explore the different types of subsetting with a simple vector, x.

x <-c(2.1, 4.2, 3.3, 5.4)

Note that the number after the decimal point represents the original position in the vector.

In x[y], what happens if x and y are different lengths? The behaviour
is controlled by the recycling rules where the shorter of the two is
“recycled” to the length of the longer. This is convenient and easy to
understand when one of x and y is length one, but I recommend avoiding
recycling for other lengths because the rules are inconsistently applied
throughout base R.

Note that a missing value in the index always yields a missing value in the output:

x[c(TRUE, TRUE, NA, FALSE)]
#> [1] 2.1 4.2 NA

Nothing returns the original vector. This is not useful for 1D vectors,
but, as you’ll see shortly, is very useful for matrices, data frames, and arrays.
It can also be useful in conjunction with assignment.

x[]
#> [1] 2.1 4.2 3.3 5.4

Zero returns a zero-length vector. This is not something you
usually do on purpose, but it can be helpful for generating test data.

x[0]
#> numeric(0)

If the vector is named, you can also use character vectors to return
elements with matching names.

NB: Factors are not treated specially when subsetting. This means that subsetting will use the underlying integer vector, not the character levels. This is typically unexpected, so you should avoid subsetting with factors:

y[factor("b")]
#> a #> 2.1

4.2.2 Lists

Subsetting a list works in the same way as subsetting an atomic vector. Using [ always return a list; [[ and $, as described in Section 4.3, let you pull out elements of a list.

4.2.3 Matrices and arrays

You can subset higher-dimensional structures in three ways:

With multiple vectors.

With a single vector.

With a matrix.

The most common way of subsetting matrices (2D) and arrays (>2D) is a simple generalisation of 1D subsetting: supply a 1D index for each dimension, separated by a comma. Blank subsetting is now useful because it lets you keep all rows or all columns.

By default, [ simplifies the results to the lowest possible dimensionality. For example, both of the following expressions return 1D vectors. You’ll learn how to avoid “dropping” dimensions in Section 4.2.5:

a[1, ]
#> A B C #> 1 4 7
a[1, 1]
#> A #> 1

Because both matrices and arrays are just vectors with special attributes, you can subset them with a single vector, as if they were a 1D vector. Note that arrays in R are stored in column-major order:

You can also subset higher-dimensional data structures with an integer matrix (or, if named, a character matrix). Each row in the matrix specifies the location of one value, and each column corresponds to a dimension in the array. This means that you can use a 2 column matrix to subset a matrix, a 3 column matrix to subset a 3D array, and so on. The result is a vector of values:

4.2.5 Preserving dimensionality

By default, subsetting a matrix or data frame with a single number, a single name, or a logical vector containing a single TRUE, will simplify the returned output, i.e. it will return an object with lower dimensionality. To preserve the original dimensionality, you must use drop = FALSE.

For matrices and arrays, any dimensions with length 1 will be dropped:

The default drop = TRUE behaviour is a common source of bugs in functions: you check your code with a data frame or matrix with multiple columns, and it works. Six months later, you (or someone else) uses it with a single column data frame and it fails with a mystifying error. When writing functions, get in the habit of always using drop = FALSE when subsetting a 2D object. For this reason, tibbles default to drop = FALSE, and [ always returns another tibble.

Factor subsetting also has a drop argument, but its meaning is rather different. It controls whether or not levels (rather than dimensions) are preserved, and it defaults to FALSE. If you find you’re using drop = TRUE a lot it’s often a sign that you should be using a character vector instead of a factor.

When extracting a single element, you have two options: you can create a smaller train, i.e., fewer carriages, or you can extract the contents of a particular carriage. This is the difference between [ and [[:

When extracting multiple (or even zero!) elements, you have to make a smaller train:

Because [[ can return only a single item, you must use it with either a single positive integer or a single string. If you use a vector with [[, it will subset recursively, i.e. x[[c(1, 2)]] is equivalent to x[[1]][[2]]. This is a quirky feature that few know about, so I recommend avoiding it in favour of purrr::pluck(), which you’ll learn about in Section 4.3.3.

While you must use [[ when working with lists, I’d also recommend using it with atomic vectors whenever you want to extract a single value. For example, instead of writing:

for (i in2:length(x)) {
out[i] <-fun(x[i], out[i -1])
}

It’s better to write:

for (i in2:length(x)) {
out[[i]] <-fun(x[[i]], out[[i -1]])
}

Doing so reinforces the expectation that you are getting and setting individual values.

4.3.2$

$ is a shorthand operator: x$y is roughly equivalent to x[["y"]]. It’s often used to access variables in a data frame, as in mtcars$cyl or diamonds$carat. One common mistake with $ is to use it when you have the name of a column stored in a variable:

(For data frames, you can also avoid this problem by using tibbles, which never do partial matching.)

4.3.3 Missing/out of bounds indices

It’s useful to understand what happens with [[ when you use an “invalid” index. The following table summarise what happens when you subset a logical vector, list, and NULL with a zero-length object (like NULL or logical()), out-of-bounds values (OOB), or a missing value (e.g. NA_integer_) with [[. Each cell shows the result of subsetting the data structure named in the row by the type of index described in the column. I’ve only shown the results for logical vectors, but other atomic vectors behave similarly, returning elements of the same type.

row[[col]]

Zero-length

OOB (int)

OOB (chr)

Missing

Atomic

Error

Error

Error

Error

List

Error

Error

NULL

NULL

NULL

NULL

NULL

NULL

NULL

If the vector being indexed is named, then the names of OOB, missing, or NULL components will be "<NA>".

The inconsistencies in the table above led to the development of purrr::pluck() and purrr::chuck(). When the element is missing, pluck() always returns NULL (or the value of the .default argument) and chuck() always throws an error. The behaviour of pluck() makes it well suited for indexing into deeply nested data structures where the component you want may not exist (as is common when working with JSON data from web APIs). pluck() also allows you to mix integer and character indices, and provides an alternative default value if an item does not exist:

4.3.4@ and slot()

There are two additional subsetting operators, which are needed for S4 objects: @ (equivalent to $), and slot() (equivalent to [[). @ is more restrictive than $ in that it will return an error if the slot does not exist. These are described in more detail in Chapter 15.

4.3.5 Exercises

Brainstorm as many ways as possible to extract the third value from the
cyl variable in the mtcars dataset.

4.4 Subsetting and assignment

All subsetting operators can be combined with assignment to modify selected values of an input vector: this is called subassignment. The basic form is x[i] <- value:

x <-1:5
x[c(1, 2)] <-c(101, 102)
x
#> [1] 101 102 3 4 5

I recommend that you should make sure that length(value) is the same as length(x[i]), and that i is unique. This is because, while R will recycle if needed, those rules are complex (particularly if i contains missing or duplicated values) and may cause problems.

With lists, you can use x[[i]] <- NULL to remove a component. To add a literal NULL, use x[i] <- list(NULL):

Subsetting with nothing can be useful with assignment because it preserves the structure of the original object. Compare the following two expressions. In the first, mtcars remains a data frame because you are only changing the contents of mtcars, not mtcars itself. In the second, mtcars becomes a list because you are changing the object it is bound to.

4.5 Applications

The principles described above have a wide variety of useful applications. Some of the most important are described below. While many of the basic principles of subsetting have already been incorporated into functions like subset(), merge(), dplyr::arrange(), a deeper understanding of how those principles have been implemented will be valuable when you run into situations where the functions you need don’t exist.

4.5.1 Lookup tables (character subsetting)

Character matching is a powerful way to create lookup tables. Say you want to convert abbreviations:

Then, let’s say we want to duplicate the info table so that we have a row for each value in grades. An elegant way to do this is by combining match() and integer subsetting (match(needles, haystack) returns the position where each needle is found in the haystack).

If you’re matching on multiple columns, you’ll need to first collapse them into a single column (with e.g. interaction()). Typically, however, you’re better off switching to a function designed specifically for joining multiple tables like merge(), or dplyr::left_join().

4.5.3 Random samples/bootstraps (integer subsetting)

You can use integer indices to randomly sample or bootstrap a vector or data frame. Just use sample(n) to generate a random permutation of 1:n, and then use the results to subset the values:

4.5.4 Ordering (integer subsetting)

To break ties, you can supply additional variables to order(). You can also change the order from ascending to descending by using decreasing = TRUE. By default, any missing values will be put at the end of the vector; however, you can remove them with na.last = NA or put them at the front with na.last = FALSE.

For two or more dimensions, order() and integer subsetting makes it easy to order either the rows or columns of an object:

You can sort vectors directly with sort(), or similarly `dplyr::arrange(), to sort a data frame.

4.5.5 Expanding aggregated counts (integer subsetting)

Sometimes you get a data frame where identical rows have been collapsed into one and a count column has been added. rep() and integer subsetting make it easy to uncollapse, because we can take advantage of rep()s vectorisation: rep(x, y) repeats x[i]y[i] times.

Remember to use the vector boolean operators & and |, not the short-circuiting scalar operators && and ||, which are more useful inside if statements. And don’t forget De Morgan’s laws, which can be useful to simplify negations:

When first learning subsetting, a common mistake is to use x[which(y)] instead of x[y]. Here the which() achieves nothing: it switches from logical to integer subsetting but the result is exactly the same. In more general cases, there are two important differences.

When the logical vector contains NA, logical subsetting replaces these
values with NA while which() simply drops these values. It’s not uncommon
to use which() for this side-effect, but I don’t recommend it: nothing
about the name “which” implies the removal of missing values.

x[-which(y)] is not equivalent to x[!y]: if y is all FALSE,
which(y) will be integer(0) and -integer(0) is still integer(0), so
you’ll get no values, instead of all values.

In general, avoid switching from logical to integer subsetting unless you want, for example, the first or last TRUE value.

4.5.9 Exercises

How would you randomly permute the columns of a data frame? (This is an
important technique in random forests.) Can you simultaneously permute
the rows and columns in one step?

How would you select a random sample of m rows from a data frame?
What if the sample had to be contiguous (i.e., with an initial row, a
final row, and every row in between)?

[ selects sub-lists: it always returns a list. If you use it with a
single positive integer, it returns a list of length one. [[ selects
an element within a list. $ is a convenient shorthand: x$y is
equivalent to x[["y"]].

Use drop = FALSE if you are subsetting a matrix, array, or data frame
and you want to preserve the original dimensions. You should almost
always use it when subsetting inside a function.

If x is a matrix, x[] <- 0 will replace every element with 0,
keeping the same number of rows and columns. In contrast, x <- 0
completely replaces the matrix with the value 0.

If you’re coming from Python this is likely to be confusing, as you’d probably expect df[1:3, 1:2] to select three columns and two rows. Generally, R “thinks” about dimensions in terms of rows and columns while Python does so in terms of columns and rows.↩

These are “pull” indices, i.e., order(x)[i] is an index of where each x[i] is located. It is not an index of where x[i] should be sent.↩